I struggle to imagine you can get a toilet in there. Looking at a washer and dryer, you need to have them along the long wall. The average washing is 30" deep, possible more. That's 2.5 feet, leaving you with 3.5 feet clearance. Unless you have a top loading washer, when the door is open, it will be probably 56" or over 4.5 feet, leaving you with a foot and a half of clearance.

Now, have some pipes and other stuff along that wall, so you may not be able to put your appliances right up against the wall, meaning you may have less clearance. So, a washer and dryer are going to be tight.

Also, is the 13' length the length of the room, which has a lot of stuff taking up the back of it or is it the open space up to the heating system?

What's pretty clear to me is that if you want both a bathroom and a laundry room, you probably aren't going to be able to put a wall between them.